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If sum of squares of zeroes of a quadrat...

If sum of squares of zeroes of a quadratic polynomial is: `p(x)=x^2-8x+k` is `-40`, then find the value of k

Text Solution

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Let `alpha` and `beta` are the zeroes of `p(x)`.
Then, `alpha+beta = -((-8))/1 = 8`
`alpha beta = k/1 = k`
Now, it is given that , `alpha^2+beta^2 = -40`
`=>(alpha+beta)^2-2alpha beta = -40`
`=>8^2-2(k) = =-40`
`=>-2k = -40-64`
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